Al-Khwārizmī's sine tables and a Western table with the Hindu norm of \(R=150\)
The authors first show that, contrary to the received opinion, al-Khwārizmī indeed did compute a summary sine table based on the Hindu value of \(R= 150\) and a detailed table based on Ptolemaic \(R= 60\). Later detailed tables based on \(R= 150\) can be easily obtained from those for \(R= 60\); this seems to be the basis of the Toledan \(R= 150\) tables. They also show an interesting error pattern in decimal tables derived from sexagesimal depending on whether there was rounding or truncation, which can be used to identify tables derived from Ptolemy's. In addition, the paper contains many remarks of interest to the student of medieval tables.
scientific article; zbMATH DE number 1931211